The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A225720 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A225720

Composite squarefree numbers n such that p+10 divides n-10 for each prime p dividing n.
(history; published version)

#13 by Charles R Greathouse IV at Sun Nov 05 00:41:57 EDT 2017

STATUS

editing

approved

#12 by Charles R Greathouse IV at Sun Nov 05 00:41:54 EDT 2017

NAME

Composite squarefree numbers n such that p(i)+10 divides n-10, where p(i) are the for each prime factors of p dividing n.

DATA

10, 79222, 206965, 784090, 1673122, 2227123, 4798090, 5202571, 9196330, 13146715, 15015430, 18213595, 19342333, 21735010, 27907435, 28234018, 28240090, 37394146, 38710990, 53990695, 54772453, 70646509, 79671826, 89678830, 107251990, 114572545, 115005187, 137245690

PROG

(PARI) is(n, f=factor(n))=if(#f[, 2]<2 || vecmax(f[, 2])>1, return(0)); for(i=1, #f~, if((n-10)%(f[i, 1]+10), return(0))); 1 \\ Charles R Greathouse IV, Nov 05 2017

EXTENSIONS

a(28) from Charles R Greathouse IV, Nov 05 2017

STATUS

approved

editing

#11 by Bruno Berselli at Fri Nov 15 05:27:16 EST 2013

STATUS

proposed

approved

#10 by Donovan Johnson at Fri Nov 15 04:59:24 EST 2013

STATUS

editing

proposed

#9 by Donovan Johnson at Fri Nov 15 04:56:17 EST 2013

DATA

EXTENSIONS

a(20)-a(27) from Donovan Johnson, Nov 15 2013

STATUS

approved

editing

#8 by T. D. Noe at Fri May 17 11:40:38 EDT 2013

STATUS

editing

approved

#7 by T. D. Noe at Fri May 17 11:40:34 EDT 2013

NAME

Composite squarefree numbers n such that p(i)+10| divides n-10, where p(i) are the prime factors of n.

CROSSREFS

Cf. A208728, A225702-A225719.

STATUS

proposed

editing

#6 by Paolo P. Lava at Fri May 17 02:35:43 EDT 2013

STATUS

editing

proposed

#5 by Paolo P. Lava at Fri May 17 02:35:39 EDT 2013

EXAMPLE

Prime factors of 2227123 are 19, 251 and 467. We have that (19+10)|( 2227123-10)/(19+10) = 76797, (251+10)|( 2227123-10)/(251+10) = 8533 and (467+10)|(2227123-10)/(467+10) = 4669.

MAPLE

for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;

if not type((n+j)/(p[d][1]-j), integer) then ok:=0; break; fi; od;

if ok=1 then print(n); fi; fi; od; end: A225720(10^9, -10);

#4 by T. D. Noe at Thu May 16 13:15:26 EDT 2013

STATUS

proposed

editing