A072502 -id:A072502 - cp's OEIS frontend

A338105 a(n) is the least integer that can be expressed as the difference of two n-gonal numbers in exactly n ways.

9, 96, 1330, 4725, 21021, 22400, 421515, 675675, 5370365, 576576, 10790325, 39255125, 51548805, 7286400, 978624647, 144729585, 649593945, 125245120, 1109593485, 4519064403, 13908638315, 253955520, 8860666815, 30587913125, 33144736086, 859541760, 147839441750

Offset: 3

Ilya Gutkovskiy, Oct 10 2020

nonn

a(17) <= 1340770739, a(18) = 144729585, a(19) <= 9381302307, a(20) <= 1257818848, a(21) <= 6299438145, a(22) <= 32911706919, a(23) <= 26720105555, a(24) <= 3141537984, a(25) <= 59558175105, a(26) <= 71119743695, a(27) <= 260207700831, a(28) <= 28582652736, a(29) <= 688883385190, a(30) <= 593086020813. - Chai Wah Wu, Oct 14 2020

			a(3) = 9 because 9 = 10 - 1 = 15 - 6 = 45 - 36 and this is the least integer that can be expressed as the difference of two triangular numbers in exactly 3 ways.

Martin Ehrenstein, Table of n, a(n) for n = 3..40
Eric Weisstein's World of Mathematics, Polygonal Number
Index to sequences related to polygonal numbers

Cf. A038547, A068314, A072502, A257411, A334034, A334035, A334036, A334037.

a(11)-a(16) from Chai Wah Wu, Oct 13 2020

a(17) and a(19)-a(40) from Martin Ehrenstein, Oct 23 2020

A267895 Numbers whose number of odd divisors is prime.

Original entry on oeis.org

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 31, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 56, 58, 59, 61, 62, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83, 86, 88, 89, 92, 94, 96, 97, 98, 100, 101, 103, 104, 106, 107, 109

Offset: 1

Omar E. Pol, Apr 04 2016

nonn

All odd primes are in the sequence.

			The divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The odd divisors of 36 are 1, 3, 9. There are 3 odd divisors of 36 and 3 is prime, so 36 is in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Complement of A267894.

Cf. A000040, A001227, A028982, A028983, A038550, A065091, A072502, A266531, A267696, A267697.

Select[Range[100], PrimeQ[DivisorSigma[0, #/2^IntegerExponent[#, 2]]] &] (* Amiram Eldar, Dec 03 2020 *)

isok(n) = isprime(sumdiv(n, d, (d%2))); \\ Michel Marcus, Apr 04 2016

cp's OEIS Frontend

A338105 a(n) is the least integer that can be expressed as the difference of two n-gonal numbers in exactly n ways.

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