A369260 -id:A369260

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A369261

Lexicographically earliest infinite sequence such that a(i) = a(j) => A324644(i) = A324644(j) and A369445(i) = A369445(j), for all i, j >= 1.

+10
3

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 15, 23, 16, 20, 24, 25, 26, 27, 21, 28, 29, 30, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 29, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 35, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 62, 53, 51, 70, 71, 72, 58, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 63 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Restricted growth sequence transform of the ordered pair [A324644(n), A369445(n)], or equally, of the pair [A000203(n), A324644(n)], or equally, of the pair [A000203(n), A369445(n)].` `For all i, j >= 1: a(i) = a(j) => A286603(i) = A286603(j).`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..65537` `Index entries for sequences related to primorial base` `Index entries for sequences related to sigma(n)`
	PROG	`(PARI)` `up_to = 65537;` `rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };` `A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };` `A324644(n) = gcd(sigma(n), A276086(n));` `Aux369261(n) = { my(u=A324644(n)); [u, sigma(n)/u]; };` `v369261 = rgs_transform(vector(up_to, n, Aux369261(n)));` `A369261(n) = v369261[n];`
	CROSSREFS	`Cf. A000203, A276086, A324644, A369445.` `Cf. also A286603, A291751, A369260 and A353523, A369047, A369051, A369062.`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jan 25 2024`
	STATUS	`approved`

A369259

Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for all i, j >= 1.

+10
2

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 15, 23, 24, 25, 26, 27, 28, 29, 21, 30, 31, 32, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 29, 31, 43, 44, 45, 46, 47, 48, 49, 46, 50, 51, 52, 53, 54, 55, 39, 56, 57, 58, 59, 60, 61, 62, 59, 46, 63, 64, 65, 66, 67, 62, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 59 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Restricted growth sequence transform of the triplet [A003557(j), A048250(i), A342671(n)].` `For all i, j >= 1:` `a(i) = a(j) => A323368(i) = A323368(j) => A291751(i) = A291751(j),` `a(i) = a(j) => A369260(i) = A369260(j) => A286603(i) = A286603(j).`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..65537` `Index entries for sequences computed from indices in prime factorization` `Index entries for sequences related to sigma(n)`
	PROG	`(PARI)` `up_to = 65537;` `rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };` `A003557(n) = (n/factorback(factor(n)[, 1]));` `A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };` `A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));` `A342671(n) = gcd(sigma(n), A003961(n));` `Aux369259(n) = [A003557(n), A048250(n), A342671(n)];` `v369259 = rgs_transform(vector(up_to, n, Aux369259(n)));` `A369259(n) = v369259[n];`
	CROSSREFS	`Cf. A000203, A001615, A003557, A003961, A048250, A286603, A291751, A369260.` `Differs from related A296089 and A323368 for the first time at n=79, where a(79) = 69, while A296089(79) = A323368(79) = 51.`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jan 25 2024`
	STATUS	`approved`

A369447

Lexicographically earliest infinite sequence such that a(i) = a(j) => A001065(i) = A001065(j) and A342671(i) = A342671(j), for all i, j >= 1.

+10
1

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 12, 24, 25, 26, 3, 27, 28, 29, 3, 30, 3, 31, 32, 33, 3, 34, 35, 36, 37, 38, 3, 39, 28, 40, 41, 42, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 51, 3, 52, 3, 31, 53, 54, 55, 56, 3, 57, 58, 59, 3, 60, 61, 62, 63, 64, 3, 65, 37, 66 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Restricted growth sequence transform of the ordered pair [A001065(n), A342671(n)].`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..65537` `Index entries for sequences computed from indices in prime factorization` `Index entries for sequences related to sigma(n)`
	PROG	`(PARI)` `up_to = 65537;` `rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };` `A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };` `Aux369447(n) = [sigma(n)-n, gcd(sigma(n), A003961(n))];` `v369447 = rgs_transform(vector(up_to, n, Aux369447(n)));` `A369447(n) = v369447[n];`
	CROSSREFS	`Cf. A000203, A001065, A003961, A342671.` `Cf. also A305801, A369260.`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jan 25 2024`
	STATUS	`approved`

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Last modified August 30 21:20 EDT 2024. Contains 375548 sequences. (Running on oeis4.)