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 A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674). 14
 1, 4, 6, 8, 14, 12, 16, 20, 30, 24, 32, 36, 40, 52, 48, 56, 100, 72, 80, 92, 96, 104, 112, 124, 136, 148, 176, 152, 214, 172, 184, 188, 262, 212, 272, 236, 248, 244, 304, 268, 346, 284, 328, 292, 386, 316, 398, 332, 376, 356, 458, 388, 478, 404, 472, 412, 526 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i. LINKS Table of n, a(n) for n=1..57. EXAMPLE The terms together with their prime indices begin: 1: {} 4: {1,1} 6: {1,2} 8: {1,1,1} 14: {1,4} 12: {1,1,2} 16: {1,1,1,1} 20: {1,1,3} 30: {1,2,3} 24: {1,1,1,2} 32: {1,1,1,1,1} 36: {1,1,2,2} 40: {1,1,1,3} 52: {1,1,6} 48: {1,1,1,1,2} MATHEMATICA nn=20; primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; wts[y_]:=Sum[(i-1)*y[[i]], {i, Length[y]}]; seq=Table[wts[primeMS[n]], {n, 1, Prime[nn]^2}]; Table[Position[seq, k][[1, 1]], {k, 0, nn}] CROSSREFS First position of n in A359674, reverse A359677. The sorted version is A359675, reverse A359680. The reverse one-based version is A359679, sorted A359754. The reverse version is A359681. The one-based version is A359682, sorted A359755. The version for standard compositions is A359756, one-based A089633. A053632 counts compositions by zero-based weighted sum. A112798 lists prime indices, length A001222, sum A056239. A124757 gives zero-based weighted sum of standard compositions, rev A231204. A304818 gives weighted sums of prime indices, reverse A318283. A320387 counts multisets by weighted sum, zero-based A359678. A358136 lists partial sums of prime indices, ranked by A358137, rev A359361. Cf. A001248, A029931, A055932, A243055, A359043, A358194, A359497, A359683. Sequence in context: A340960 A261680 A218465 * A050902 A320125 A110974 Adjacent sequences: A359673 A359674 A359675 * A359677 A359678 A359679 KEYWORD nonn,look AUTHOR Gus Wiseman, Jan 14 2023 STATUS approved

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Last modified March 2 09:28 EST 2024. Contains 370461 sequences. (Running on oeis4.)